Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.4 LIQUID ANDSOLIDMIXTURES OFNONELECTROLYTES 245

where the quantityBi^0 , in order to be consistent withViD.@V=@ni/T;p;nj§i, is found to
be given by
Bi^0 D 2

X

j

yjBijB (9.3.26)

For the constituents of a binary mixture of A and B, Eq.9.3.26becomes

BA^0 DBAAC.BAAC2BABBBB/yB^2 (9.3.27)

(binary gas mixture)

BB^0 DBBBC.BAAC2BABBBB/yA^2 (9.3.28)

(binary gas mixture)

When we substitute the expression of Eq.9.3.25forViin Eq.9.3.18, we obtain a relation
between the fugacity coefficient of constituentiand the functionBi^0 :

lniD

Bi^0 p

RT

(9.3.29)

The third column of Table9.1gives formulas for various partial molar quantities of
constituentiin terms ofBi^0 and its temperature derivative. The formulas are the same as the
approximate formulas in the third column of Table7.5for molar quantities of apuregas,
withBi^0 replacing the second virial coefficientB.

9.4 Liquid and Solid Mixtures of Nonelectrolytes

Homogeneous liquid and solid mixtures are condensed phases of variable composition.
Most of the discussion of condensed-phase mixtures in this section focuses on liquids.
The same principles, however, apply to homogeneous solid mixtures, often called solid
solutions. These solid mixtures include most metal alloys, many gemstones, and doped
semiconductors.
The relations derived in this section apply to mixtures of nonelectrolytes—substances
that do not dissociate into charged species. Solutions of electrolytes behave quite differently
in many ways, and will be discussed in the next chapter.

9.4.1 Raoult’s law

In 1888, the French physical chemist Franc ̧ois Raoult published his finding that when a
dilute liquid solution of a volatile solvent and a nonelectrolyte solute is equilibrated with a
gas phase, the partial pressurepAof the solvent in the gas phase is proportional to the mole
fractionxAof the solvent in the solution:

pADxApA (9.4.1)

HerepAis the saturation vapor pressure of the pure solvent (the pressure at which the pure
liquid and pure gas phases are in equilibrium).
In order to place Raoult’s law in a rigorous thermodynamic framework, consider the
two systems depicted in Fig.9.5on the next page. The liquid phase of system 1 is a binary